A box has a wall on every side, so its inside is the outside minus two walls. To fit something inside, start from the thing: its size, plus a gap each side, plus a wall each side, gives the outside.
Your Arduino needs a case. You print a box 'about the right size', and it's 2 mm too small. Plastic is cheap; your time and the printer's aren't. How do you get it right first time?
Every measurement here is in millimetres. In Tinkercad you set a shape's size by typing in its dimension boxes, and you make a hollow box by grouping a solid box with a slightly smaller "hole" box.
Predict: Read the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Try: Try it on the board and compare the result with your prediction.
Investigate: Work out why it happens, one step at a time.
Modify: Change the problem on purpose and see what happens.
Practise: A few on your own, to check you have it.
Make: Make your own problem using what you have learned. Expect a few tries; that is normal.
WidthMore contexts, same idea.
Make your prediction first. Help opens once you've locked it in.
PredictRead the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Inside width
TryTry it on the board and compare the result with your prediction.
Try: walls and inside
Try it yourselfYour edits are saved in this browser.
Make the walls 3 mm. How much did the inside width shrink?
Use the board. This ticks when you get there.
Now change the outside width so the inside is exactly 60 mm (walls still 3 mm).
Use the board. This ticks when you get there.
InvestigateWork out why it happens, one step at a time.
Worked example: a case for an Uno
Worked exampleBefore each step, say what you think comes next.
Uno width=68.6Start from what goes inside.
68.6+2×1=70.6A 1 mm gap on each side: the inside width.
70.6+2×2=74.6A 2 mm wall on each side: the outside width.
74.6→75Round up to a size you can set (never down).
Now the depth.
The Uno is 53.4 mm deep. With a 1 mm gap and a 2 mm wall each side, how deep is the case outside (mm)?
Sam's 57 mm part won't go in. Click the line where Sam's working first goes wrong.
ModifyChange the problem on purpose and see what happens.
Vary: change one thing
Try it yourselfYour edits are saved in this browser.
Set the outside size so the Uno fits with 1 to 1.5 mm to spare on the tightest side (2 mm walls).
Use the board. This ticks when you get there.
Now make the walls 3 mm for a tougher case, keeping a 1 to 1.5 mm gap.
Use the board. This ticks when you get there.
Modify TypicalChange the problem on purpose and see what happens.
Build it in Tinkercad
PractiseA few on your own, to check you have it.
Sizes
A box is 80 mm outside with 2.5 mm walls. Inside width (mm)?
A 30 mm part, a 0.5 mm gap each side, 2 mm walls. Outside width (mm)?
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
The smallest case
Try it yourselfYour edits are saved in this browser.
Need a hint?
Walls 1.5 mm, gap at least 0.5 mm on the tightest side.
Another hint
Width: 68.6 + 2 × 0.5 + 2 × 1.5 = 72.6, so 73 on a 0.5 mm slider.
Another hint
Depth: 53.4 + 1 + 3 = 57.4, so 57.5.
Make the smallest case you can with 1.5 mm walls and at least 0.5 mm to spare: no more than 73 × 58 mm.
Use the board. This ticks when you get there.
For teachers
Students find a box's inside size from its outside and walls, design a case for an Uno from the part outwards (part, gap, wall), meet Sam's one-wall slip, change the wall thickness, build the case in Tinkercad 3D by typed dimensions, and find the smallest case that fits. About 40 minutes.
I can work out a box's inside from its outside and walls.
I can design a case from the part outwards.
I can set exact sizes in Tinkercad.
Before class
The board is a 2D top view; heights work the same way (a floor and a lid instead of side walls). Measure the real part with calipers if you have them: published sizes don't include sockets that stick out (the Uno's USB and power sockets do). Tinkercad: the same class code as Circuits.
Running the lesson
Predict: draw a box on the board and point at both walls.
Worked example: write it outwards, live.
Tinkercad: ask why the hole box is placed 2 mm in and up.
The hard part (on purpose)
Students drag shapes to 'about right'. Make typing dimensions the rule.
When students get stuck
A student's case is 2 mm too small. Ask: How many walls does a box have across its width? Fix: Two: subtract (or add) both.
Stretch and support
Stretch: Add holes in the case wall for the Uno's USB and power sockets, measured from the board's edge.
Support: A drawn cross-section with part, gap and wall labelled on both sides.
inside width: Committing to the inside width tests the new move: a wall on each side comes off.
Try: walls and inside: Changing the wall on the board settles the prediction: the inside shrinks by twice the change.
Worked example: a case for an Uno: Working outwards from the part (part + gaps + walls) models the move; Sam's one-wall slip is planted after the method.
Vary: change one thing: Designing the case on the board, then changing only the wall, shows the outside must grow by twice the change to keep the same gap.
Build it in Tinkercad: Building the hollow box in Tinkercad by typing dimensions (not dragging) is the habit that makes parts fit.
sizes: Inside and outside both ways.
the smallest case: Finding the smallest case that still fits reverses the process: start from a limit and work back to the dimensions.
Now you can
Work out a box's inside from its outside and walls.